Practice Problems: Load Calculations

Table of Contents
1. Question 1
2. Question 2
3. Question 3
4. Question 4
5. Question 5
6. Question 6
7. Question 7
8. Question 8
9. Question 9
10. Question 10
11. Question 11
12. Question 12
13. Question 13
14. Question 14
15. Question 15
16. Question 16
17. Question 17
18. Question 18
19. Question 19
20. Question 20
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Question 1

A mechanical engineer is designing the HVAC system for a commercial office building located in Chicago, IL. The building has a south-facing glass curtain wall with the following specifications:
- Wall area: 2,400 ft²
- Glass type: Double-pane with U-factor = 0.35 Btu/(hr·ft²·°F)
- Winter design outdoor temperature: -5°F
- Indoor design temperature: 70°F
- Solar heat gain coefficient (SHGC): 0.40
What is the peak conductive heat loss through the curtain wall during winter design conditions?
(a) 54,000 Btu/hr
(b) 63,000 Btu/hr
(c) 72,000 Btu/hr
(d) 81,000 Btu/hr

Question 2

A facilities engineer is calculating the cooling load for a data center in Phoenix, AZ. The room contains the following equipment:
- 50 servers, each rated at 850 W
- 10 networking switches, each rated at 250 W
- Lighting load: 15,000 W
- Occupancy: 4 people (sensible heat: 250 Btu/hr per person, latent heat: 200 Btu/hr per person)
Assuming all equipment operates at rated capacity and 10% safety factor, what is the total sensible cooling load in tons of refrigeration?
(a) 16.2 tons
(b) 17.8 tons
(c) 19.5 tons
(d) 21.3 tons

Question 3

A consulting engineer is performing heat loss calculations for a warehouse with the following roof specifications:
- Roof area: 12,000 ft²
- Roof construction: Built-up roof with R-value of 25 hr·ft²·°F/Btu
- Indoor temperature: 65°F
- Outdoor design temperature: 15°F
- Ceiling height variation causes 15% additional heat loss
What is the total roof heat loss including the additional losses?
(a) 22,080 Btu/hr
(b) 24,000 Btu/hr
(c) 27,600 Btu/hr
(d) 30,240 Btu/hr

Question 4

A mechanical engineer is sizing equipment for a restaurant kitchen in Miami, FL. The kitchen has the following appliances operating during peak hours:
- Gas range: 80,000 Btu/hr input, 40% radiant heat
- Convection oven: 35,000 Btu/hr input, 50% radiant heat
- Dishwasher: 12 kW electric, 60% sensible heat
- Hood exhaust removes 50% of appliance heat gains
What is the net sensible heat gain to the space in Btu/hr?
(a) 54,850 Btu/hr
(b) 69,280 Btu/hr
(c) 82,100 Btu/hr
(d) 95,560 Btu/hr

Question 5

A project engineer is calculating infiltration loads for a warehouse with the following characteristics:
- Volume: 450,000 ft³
- Air changes per hour (ACH): 0.5
- Outdoor temperature: 95°F, humidity ratio: 0.018 lb_w/lb_da
- Indoor temperature: 75°F, humidity ratio: 0.009 lb_w/lb_da
- Air density: 0.075 lb/ft³, specific heat: 0.24 Btu/(lb·°F)
What is the sensible infiltration load?
(a) 40,500 Btu/hr
(b) 50,625 Btu/hr
(c) 60,750 Btu/hr
(d) 70,875 Btu/hr

Question 6

A building engineer is evaluating solar heat gain through a west-facing window in Dallas, TX. The window specifications are:
- Window area: 120 ft²
- Solar heat gain coefficient (SHGC): 0.32
- Peak solar radiation on west wall: 216 Btu/(hr·ft²)
- Internal shading coefficient: 0.85
- Cooling load factor (CLF) for west exposure at 4 PM: 0.76
What is the instantaneous cooling load from solar heat gain?
(a) 5,350 Btu/hr
(b) 6,730 Btu/hr
(c) 8,280 Btu/hr
(d) 10,560 Btu/hr

Question 7

A mechanical engineer is designing the heating system for an industrial facility. The building has the following wall section:
- Exterior brick: 4 inches, k = 0.42 Btu/(hr·ft·°F)
- Air space: R = 1.0 hr·ft²·°F/Btu
- Insulation: 3 inches, k = 0.025 Btu/(hr·ft·°F)
- Interior gypsum: 0.5 inches, k = 0.10 Btu/(hr·ft·°F)
- Inside air film: R = 0.68, Outside air film: R = 0.17
What is the overall U-factor of this wall assembly in Btu/(hr·ft²·°F)?
(a) 0.062
(b) 0.074
(c) 0.086
(d) 0.098

Question 8

A facilities manager is calculating the cooling load for a conference room with the following occupancy schedule:
- Maximum occupancy: 40 people
- Meeting duration: 3 hours starting at 2 PM
- Sensible heat gain per person: 250 Btu/hr
- Latent heat gain per person: 200 Btu/hr
- Room cooling load factor (CLF) at peak: 0.88
- Building type: Medium weight construction
What is the total sensible cooling load from occupancy at peak conditions?
(a) 7,920 Btu/hr
(b) 8,800 Btu/hr
(c) 10,000 Btu/hr
(d) 11,360 Btu/hr

Question 9

A consulting engineer is designing a ventilation system for a manufacturing space. The specifications are:
- Required outdoor air: 3,500 CFM
- Outdoor conditions: 92°F DB, 75°F WB
- Indoor conditions: 75°F DB, 50% RH
- Enthalpy of outdoor air: 38.6 Btu/lb_da
- Enthalpy of indoor air: 28.2 Btu/lb_da
- Air density: 0.074 lb/ft³
What is the total cooling load from outdoor air ventilation in tons?
(a) 5.2 tons
(b) 6.8 tons
(c) 8.1 tons
(d) 9.4 tons

Question 10

A project engineer is calculating heat loss through a basement floor slab for a residential building. The specifications are:
- Slab area: 1,800 ft²
- Slab perimeter: 180 ft
- Indoor temperature: 70°F
- Ground temperature: 50°F
- Perimeter heat loss coefficient: 0.68 Btu/(hr·ft·°F)
- Slab is uninsulated
What is the total heat loss through the basement slab perimeter?
(a) 1,850 Btu/hr
(b) 2,448 Btu/hr
(c) 3,060 Btu/hr
(d) 3,672 Btu/hr

Question 11

A mechanical engineer is sizing a cooling system for a computer lab with the following loads:
- 30 desktop computers: 200 W each (85% sensible)
- 30 monitors: 65 W each (100% sensible)
- Lighting: 3.5 W/ft² over 1,200 ft² area
- Occupancy: 30 students at 275 Btu/hr sensible each
- Diversity factor for computers: 0.75
What is the total sensible heat gain in Btu/hr?
(a) 38,450 Btu/hr
(b) 42,920 Btu/hr
(c) 47,385 Btu/hr
(d) 51,840 Btu/hr

Question 12

A facilities engineer is evaluating heat gain through a flat roof in Houston, TX. The roof details are:
- Roof area: 8,500 ft²
- U-factor: 0.048 Btu/(hr·ft²·°F)
- Sol-air temperature at peak: 145°F
- Indoor temperature: 75°F
- Cooling load temperature difference (CLTD): 58°F
- Roof is dark-colored with no ventilation
What is the cooling load from the roof using the CLTD method?
(a) 23,460 Btu/hr
(b) 23,664 Btu/hr
(c) 28,560 Btu/hr
(d) 33,456 Btu/hr

Question 13

A design engineer is calculating the latent cooling load for a gymnasium with the following parameters:
- Occupancy: 120 people exercising
- Latent heat gain per person: 625 Btu/hr
- Pool evaporation: 45 lb/hr of water
- Latent heat of vaporization: 1,050 Btu/lb
- Shower areas add 15% to total latent load
What is the total latent cooling load in Btu/hr?
(a) 115,000 Btu/hr
(b) 128,400 Btu/hr
(c) 140,850 Btu/hr
(d) 154,200 Btu/hr

Question 14

A mechanical engineer is analyzing conduction heat gain through an exterior wall in Atlanta, GA. The wall specifications are:
- Wall area: 1,500 ft²
- Overall U-factor: 0.082 Btu/(hr·ft²·°F)
- Outdoor design temperature: 95°F
- Indoor design temperature: 75°F
- Wall faces east with morning sun exposure
- CLTD for this wall orientation at 3 PM: 28°F
What is the cooling load through the wall at 3 PM?
(a) 2,460 Btu/hr
(b) 3,444 Btu/hr
(c) 4,920 Btu/hr
(d) 5,535 Btu/hr

Question 15

A consulting engineer is performing load calculations for a retail store with the following lighting system:
- Fluorescent fixtures: 180 fixtures × 128 W each
- LED display lighting: 4,500 W
- Operating hours: 12 hours/day
- Ballast factor for fluorescent: 1.18
- Space use factor: 0.92
- Cooling load factor at peak hour: 0.85
What is the instantaneous cooling load from lighting at peak conditions in Btu/hr?
(a) 82,560 Btu/hr
(b) 89,440 Btu/hr
(c) 95,820 Btu/hr
(d) 102,350 Btu/hr

Question 16

A project engineer is calculating transmission heat loss for a cold storage facility. The wall specifications are:
- Wall area: 3,200 ft²
- Wall construction: 6-inch polyurethane insulation, k = 0.016 Btu/(hr·ft·°F)
- Interior surface: R = 0.45 hr·ft²·°F/Btu
- Exterior surface: R = 0.25 hr·ft²·°F/Btu
- Interior temperature: -10°F
- Exterior temperature: 85°F
What is the heat gain through the wall?
(a) 3,840 Btu/hr
(b) 4,560 Btu/hr
(c) 5,280 Btu/hr
(d) 6,080 Btu/hr

Question 17

A mechanical engineer is sizing a heating system for a warehouse in Minneapolis, MN. The building parameters are:
- Volume: 720,000 ft³
- Infiltration rate: 0.75 air changes per hour
- Outdoor design temperature: -15°F
- Indoor design temperature: 60°F
- Air density: 0.078 lb/ft³
- Specific heat of air: 0.24 Btu/(lb·°F)
What is the heating load due to infiltration?
(a) 75,600 Btu/hr
(b) 90,720 Btu/hr
(c) 100,440 Btu/hr
(d) 115,560 Btu/hr

Question 18

A facilities engineer is evaluating heat gain from motors in a mechanical room with the following equipment:
- Chilled water pump: 25 HP motor, 92% efficient, 85% load factor
- Condenser water pump: 30 HP motor, 91% efficient, 90% load factor
- Air handling unit fans: Two 15 HP motors, 90% efficient each, 75% load factor
- Motor heat gain: All motors are located in conditioned space
What is the total heat gain from all motors in Btu/hr?
(a) 142,500 Btu/hr
(b) 156,800 Btu/hr
(c) 168,450 Btu/hr
(d) 182,300 Btu/hr

Question 19

A design engineer is calculating heat gain through a skylight in a commercial building. The skylight specifications are:
- Skylight area: 450 ft²
- U-factor: 0.58 Btu/(hr·ft²·°F)
- SHGC: 0.48
- Peak solar radiation on horizontal surface: 248 Btu/(hr·ft²)
- Outdoor temperature: 93°F
- Indoor temperature: 75°F
- CLF for skylight: 0.82
What is the total instantaneous cooling load through the skylight?
(a) 48,560 Btu/hr
(b) 54,220 Btu/hr
(c) 59,880 Btu/hr
(d) 65,540 Btu/hr

Question 20

A mechanical engineer is designing a ventilation system for a laboratory building. The requirements are:
- Required outdoor air flow: 2,800 CFM
- Outdoor conditions: 35°F DB, 28°F WB
- Indoor conditions: 70°F DB, 40% RH
- Enthalpy of outdoor air: 12.8 Btu/lb_da
- Enthalpy of indoor air: 24.4 Btu/lb_da
- Specific volume of air: 13.2 ft³/lb_da
What is the heating load required to condition the outdoor air in Btu/hr?
(a) 14,760 Btu/hr
(b) 18,480 Btu/hr
(c) 22,200 Btu/hr
(d) 25,920 Btu/hr